Details

sample43.0ms

Algorithm

intervals

Results

20.0ms	91×	body	1280	valid
9.0ms	127×	body	80	valid
3.0ms	17×	body	640	valid
2.0ms	19×	body	320	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 17.5b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.7b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`times-frac`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 54

Calls

3 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series162.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(/ 1.0 (hypot 1.0 x))
83.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	200	410
1	601	393
2	1999	391
3	5001	391

prune111.0ms

Filtered

63 candidates to 45 candidates (71.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	2	64

Merged error: 17.0b

Counts

64 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.2b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
8×	`add-exp-log` `associate-*r/` `add-cbrt-cube` `add-log-exp`
7×	`associate-/r*`
6×	`associate-/l*`
5×	`distribute-lft-out`
4×	`pow1` `flip3--` `associate--l+` `frac-sub` `flip--` `associate-/l/`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv`
1×	`+-commutative` `diff-log` `div-sub` `sum-log`

Counts

4 → 95

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
13.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
79.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
160.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify53.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	423	1277
1	1641	1179
2	5001	1174

prune228.0ms

Filtered

107 candidates to 77 candidates (72.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	106	3	109

Merged error: 17.0b

Counts

109 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.2b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.2b	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
28×	`times-frac`
24×	`add-sqr-sqrt` `add-cube-cbrt` `log-pow`
18×	`exp-prod`
10×	`pow1`
9×	`log-prod` `distribute-lft-out`
8×	`associate--l+` `add-log-exp`
7×	`associate-/l*`
6×	`add-exp-log` `sub-neg` `exp-sum` `add-cbrt-cube`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-/r`
2×	`log-div` `flip3--` `flip3-+` `exp-diff` `associate-/r/` `frac-sub` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `diff-log` `div-sub` `div-exp` `rem-log-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 106

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
13.0ms	(/ (log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
7.0ms	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
162.0ms	(/ (log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
38.0ms	(log (exp (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	386	1832
1	1299	1660
2	5001	1650

prune235.0ms

Filtered

118 candidates to 76 candidates (64.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	118	3	121

Merged error: 17.0b

Counts

121 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(* (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.7b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.7b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
30×	`sqrt-prod`
20×	`add-cube-cbrt`
19×	`pow1`
12×	`sqrt-div` `swap-sqr`
9×	`times-frac`
8×	`add-exp-log` `flip3--` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `add-cbrt-cube` `flip--` `distribute-lft-out--` `add-log-exp`
6×	`difference-of-squares`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `pow-sqr` `associate-/l`
2×	`sub-neg` `diff-log` `associate-r/` `associate-l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 120

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
12.0ms	(* (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
84.0ms	(* (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
85.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
84.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	255	1307
1	1042	1197
2	5001	1153

prune243.0ms

Filtered

132 candidates to 75 candidates (56.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	132	3	135

Merged error: 17.0b

Counts

135 → 3

regimes122.0ms

Accuracy

0% (0.0b remaining)

Error of 14.6b against oracle of 14.6b and baseline of 14.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	13
1	19	13

end0.0ms

sample1.1s

Algorithm

intervals

Results

614.0ms	2768×	body	1280	valid
166.0ms	4144×	body	80	valid
106.0ms	615×	body	640	valid
36.0ms	293×	body	320	valid
14.0ms	180×	body	160	valid